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Rooney,Inc.is considering the purchase of a new machine costing $640,000.The machine's useful life is expected to be 8 years with no salvage value.The straight-line depreciation method will be used.The net increase in annual after tax cash flow is expected to be $147,000.Rooney estimates its cost of capital to be 14%.(The present value of a $1 annuity for 8 years at 14% is 4.639,and the present value of $1 to be received in 8 years is 0.351. )
-Upper level managers at Rooney,Inc.are concerned that employee estimates of future cash flows from the new machine may be overly optimistic.To what dollar amount can the annual after tax cash flow fall before the investment in the new machine should be rejected?

Question

Quizplus · Accepted Answer

To calculate the maximum allowable decline in annual after-tax cash flow, we need to use the net present value (NPV) formula and solve for the cash flow variable:
NPV = -Cost + ∑(Cash flows / (1 + r)^t)
0 = -640,000 + ∑(147,000 / (1 + 0.14)^t)
Solving for the cash flow variable:
147,000 / (1 + 0.14)^t = 640,000 / 4.639
147,000 / (1 + 0.14)^t = 138,118.95
(1 + 0.14)^t = 1.063587
t = ln(1.063587) / ln(1 + 0.14)
t ≈ 5.6 years
So, the maximum allowable decline in annual after-tax cash flow can be calculated as follows:
Max decline = (147,000 / (1 + 0.14)^5.6) - 147,000
Max decline ≈ $137,961
Therefore, the investment in the new machine should be rejected if the annual after-tax cash flow falls by more than $137,961. Answer choice D is correct.

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